Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 257

F "
l

F #
l

cloud cover in layer i , the cloudy upward and downward fluxes are then

w w

expressed as:

N X

F l w .i/ D .1 CC N;i /F 0 .i/ C .CC i;k C 1 CC i;k /F k .i/ (11.14)

k D i

i X

F l w .i/ D .1 CC i 1;0 /F 0 .i/ C .CC i;k C 1 CC i;k /F k .i/

(11.15)

k D 1

where CC i;j is the cloudiness encountered between any two levels i and j in the

atmosphere computed using the overlap assumption described below.
In the case of semi-transparent clouds, the fractional cloudiness entering the
calculations is an effective cloud cover equal to the product of the emissivity due
to condensed water and gases in the layer by the horizontal coverage of the cloud
cover. This is the so called effective emissivity approach.
To reduce a computational cost of the linearized LW radiation for data assim-
ilation, the scheme is not called at each time step. Furthermore, the transmission
functions are only computed for H 2 OandCO 2 absorbers (though the version taking
into account the whole spectrum of absorbers is also coded for aerosols and other
gases). The cloud effects on LW radiation are only computed up to cloud top.

Cloud Overlap Assumptions

Cloud overlap assumptions must be made in atmospheric models in order to
organize the cloud distribution used for radiation. This is is necessary to account
for the fact that clouds often do not fill the whole grid box. The maximum-
random overlap assumption (originally introduced in Geleyn and Hollingsworth
1997 ) is used operationally ( Morcrette and Jakob 2000 ). Adjacent cloudy layers are
combined by assuming maximum overlap to form a contiguous cloud and discrete
layers separated by clear-sky are combined randomly.

Cloud Optical Properties

When one considers cloud-radiation interactions, it is not only the cloud fraction
or cloud volume, but also cloud optical properties that matter. In the case of SW
radiation, cloud radiative calculations depend on three different parameters: the
optical thickness, the asymmetry factor and the single scattering albedo. They are
derived from Fouquart ( 1987 ) for water clouds, and Ebert and Curry ( 1992 )forice
clouds. They are functions of cloud condensate and a specified effective radius.
Cloud LW optical properties are represented by the emissivity, related to the
condensed water amount, and by the condensed-water mass absorption coefficient
obtained from Smith and Shi ( 1992 ) for water clouds and Ebert and Curry ( 1992 )
for ice clouds.